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Abstract

Self-sustained order can emerge in complex systems due to internal feedback between coupled subsystems. Here, we present our discovery of a nonmonotonic emergence of order amidst chaos in a turbulent thermoacoustic fluid system. Fluctuations play a vital role in determining the dynamical state and transitions in a system. In this work, we use complex networks to encode jumps in amplitude scales owing to fluctuations as links between nodes representing amplitude bins. The number of possible amplitude transitions at a fixed timescale reflects the complexity of dynamics at that timescale. The network entropy quantifies the number of and uncertainty associated with such transitions. Using network entropy, we show that the uncertainty in fluctuations first increases and then decreases as the system transitions from chaos via intermittency to order. The competition between turbulence and nonlinear interactions leads to such nonmonotonic emergence of order amidst chaos in turbulent thermoacoustic fluid systems.